I love the Google Slides app on my phone. It is Google Drive, filtered for Google Slides. I can create new Google Slides or access ones I have already created.
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No Save Button
Just like on the browser anything I make in Google Slides on my phone is automatically saved. I can go to my laptop later and find the Slides no problem.
The default for a new Google Slides is a name of Untitled Presentation. You can change the presentation name by tapping in the upper left on the title.
If you have put a title on the first slide the presentation name will default to this. Very handy. In fact, this is my default. I first double tap on the title text box on the first slide and then tap on the “Untitled Presentation” in the upper left corner.
In Google Docs you rename the file using the menu. Not in Google Slides. The behavior more closely mimics the browser version of Google Slides.
For presentations you make on your phone they are by default available Offline. Very handy when you are getting on a plane or have low connectivity. The presentations will automatically sync when you have data or wifi available. No extra action required.